Difference between revisions of "Variance:Probability and Statistics"
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(New page: {{math-h}} '''Variance''' is a measure in statistics of the dispersion of a set of values (represented as <math>X</math>). It is defined as :<math>\sigma^2 = \operat...) |
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The formula for variance must not be confused with the formula | The formula for variance must not be confused with the formula | ||
| − | :<math>S_{n}^2 = {\sum_n( | + | :<math>S_{n}^2 = {\sum_n(X_n - \bar X)^2 \over n - 1}</math> |
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| + | (where <math>\bar X = {\sum_n X_n \over N}</math> is the [[sample mean]]). | ||
which is the formula for a [[point estimate]] of the true variance from a sample of size ''n''. As such this estimator itself has a variance which, as the formula indicates, decreases as the sample size increases. | which is the formula for a [[point estimate]] of the true variance from a sample of size ''n''. As such this estimator itself has a variance which, as the formula indicates, decreases as the sample size increases. | ||
Revision as of 15:32, January 19, 2009
| <math>\frac{d}{dx} \sin x=?\,</math> | This article/section deals with mathematical concepts appropriate for late high school or early college. |
Variance is a measure in statistics of the dispersion of a set of values (represented as <math>X</math>). It is defined as
- <math>\sigma^2 = \operatorname{E}[(X-\operatorname{E}[X])^2] = \operatorname{E}[X^2] - (\operatorname{E}[X])^2</math>
where the expected value of X is E(X).
The formula for variance must not be confused with the formula
- <math>S_{n}^2 = {\sum_n(X_n - \bar X)^2 \over n - 1}</math>
(where <math>\bar X = {\sum_n X_n \over N}</math> is the sample mean).
which is the formula for a point estimate of the true variance from a sample of size n. As such this estimator itself has a variance which, as the formula indicates, decreases as the sample size increases.